Write an inequality to represent
“three-fourths of a number, n, is
greater than 27.”

Separate the variables:

[tex]y' = \dfrac{dy}{dx} = (y+1)(y-2) \implies \dfrac1{(y+1)(y-2)} \, dy = dx[/tex]

Separate the left side into partial fractions. We want coefficients a and b such that

[tex]\dfrac1{(y+1)(y-2)} = \dfrac a{y+1} + \dfrac b{y-2}[/tex]

[tex]\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}[/tex]

[tex]\implies 1 = a(y-2)+b(y+1)[/tex]

[tex]\implies 1 = (a+b)y - 2a+b[/tex]

[tex]\implies \begin{cases}a+b=0\\-2a+b=1\end{cases} \implies a = -\dfrac13 \text{ and } b = \dfrac13[/tex]

So we have

[tex]\dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = dx[/tex]

Integrating both sides yields

[tex]\displaystyle \int \dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = \int dx[/tex]

[tex]\dfrac13 \left(\ln|y-2| - \ln|y+1|\right) = x + C[/tex]

[tex]\dfrac13 \ln\left|\dfrac{y-2}{y+1}\right| = x + C[/tex]

[tex]\ln\left|\dfrac{y-2}{y+1}\right| = 3x + C[/tex]

[tex]\dfrac{y-2}{y+1} = e^{3x + C}[/tex]

[tex]\dfrac{y-2}{y+1} = Ce^{3x}[/tex]

With the initial condition y(0) = 1, we find

[tex]\dfrac{1-2}{1+1} = Ce^{0} \implies C = -\dfrac12[/tex]

so that the particular solution is

[tex]\boxed{\dfrac{y-2}{y+1} = -\dfrac12 e^{3x}}[/tex]

It's not too hard to solve explicitly for y; notice that

[tex]\dfrac{y-2}{y+1} = \dfrac{(y+1)-3}{y+1} = 1-\dfrac3{y+1}[/tex]

Then

[tex]1 - \dfrac3{y+1} = -\dfrac12 e^{3x}[/tex]

[tex]\dfrac3{y+1} = 1 + \dfrac12 e^{3x}[/tex]

[tex]\dfrac{y+1}3 = \dfrac1{1+\frac12 e^{3x}} = \dfrac2{2+e^{3x}}[/tex]

[tex]y+1 = \dfrac6{2+e^{3x}}[/tex]

[tex]y = \dfrac6{2+e^{3x}} - 1[/tex]

[tex]\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}[/tex]

Answer:

2.24

Step-by-step explanation:

Well...Ummm I don't know how to exactly explain it but I'll try

11 x 2.24=24.64 or you can do division and do 24.64 divided by 2.24=24.64

Answer:

I thino the awnser is 103.5

Step-by-step explanation:

Answer:

[tex]let \:A= The\: amplitude\: of\: the\: graph \\ because \: \: \: a = \frac{1}{2} (y \: axis - y \: axis) \\ therefore \: \: a = \frac{1}{2} (0 - ( - 41) = 2[/tex]

Answer:

12/4. & 22/5

Step-by-step explanation:

3 2/4 you have to multiply 3x4 which equals to 12 then you add 2. your answers is 14 but you need to keep the denominator 4. your final answer is 12/4. this is the improper fraction. you do the same to 4 2/5.

The ratio of the fraction in the simplest form is 24 /5.

Fractions are non integers. They are made up of and denominators. An example of a fraction is 2/3. 2 is the numerator and 3 is the denominator.

In order to express in the simplest form, divide both the numerator and denominator by similar factors.

96 : 20 = 96/20 = 24/5

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Using the Central Limit Theorem, it is found that:

a) The shape is approximately normal.

b) It targets the population mean.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

Item a:

The variable is skewed, however, the sample size is greater than 30, hence the approximate shape of the distribution is normal.

Item b:

According to the mean of the sampling distributions, given by the Central Limit Theorem, it targets the population mean.

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Answer:

Step-by-step explanation:

X would be adults Y would be children

3x+3y=35

2x+4y=25

One of the variables have to be equal to each other. So multiply all the terms in the bottom equation by 1.5

You get 3x+6y=37.5

Subtract one equation from another

3x+3y=35

3x+6y=37.5

You get 3y=2.5

Divide both sides by 3
y = 5/6

Now do the same but for X

Multiply the equation by 4/3

4x+4y=46 2/3

Minus the other equation

2x=21 2/3

Divide by 2

x = 10 5/6

Plug numbers in to double check, and they check out

Answer:

B

Step-by-step explanation:

The answer is B 19%.

Answer:

b.19%

Step-by-step explanation:

hope this will help you

Answer:

30

Step-by-step explanation:

Use PEMDAS

parentheses is first

3+7=10

There's no exponents

You have to do it in order from left to right

6÷2=3

3*10=30

Answer:

The answer is 30.

First, start with 3 plus 7...that gives you 10. Then, 6 divided by 2 is 3. Lastly, multiply 10 by 3 and you've got 30!

If you can, please mark me brainliest!

Step-by-step explanation:

a² = a × a

a > 1

a² = (1+d) × (1+d) = 1² + 2d + d²

with d > 0

since d > 0, then so is 2d and also d².

so, a² is the sum of 1² = 1 and something greater than 0.

so, a² > 1

Given :-

To Find :-

Solution :-

Here a equation is given to us and we need to find out the slope of the line . The given equation is ,

→ y = -1/2x + 1/4

We know that slope intercept form of the line is ,

→ y = mx + c

where m is the slope of the line .

On comparing ,

→ m = -1/2

Hence the slope of the line is -1/2.

I hope this helps .

Answer:

r e^iT = r cos T + i r sin T

r cos T = -1

r sin T = sqrt 3

30, 60 90 triangle in second quadrant r = 2, T = 180-60 = 120

so

2e^120i

foruth root is 2^.25 e^(120/4)i

2^.25 e^30 i

2^.25 ( cos 30 + i sin 30)

Step-by-step explanation:

Answer:

equation: 2(Y-7) = 9

Answer:

A. E bisects AB and CD

Step-by-step explanation:

If E is a bisector, it creates two pairs of congruent sides. The included angles are congruent because they are vertical angles. The triangles will be congruent by SAS.

Answer:

A

Step-by-step explanation:

Sum of angles in a straight line is 180°

180° - 64° = 116°

Answer:

Surds

√3×√3 =3

3√6 × 4√6 =12 × 6= 72

(2√7)²=(2√7)(2√7)=4+2√7+2√7+7=4√7 +11

√5 ×√5 ×√5 =5√5

Based on the division computed, the number of packages is 63 and there will be a remainder of 3.

From the question, we are informed that Evan has 381 bagels to put into packages and that each package must hold 6 bagels.

The number of packages will be:

= 381/6

= 63 packages

It should also be noted that there will be a remainder of 3 bagels left.

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Answer: The number of packages is 63 and there will be a remainder of 3

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

Answer:

16 oatmeal cookies

Step-by-step explanation:

We can represent this situation as an equation.

Step 1: Add 7 to both sides.

Therefore, Lisa baked 16 oatmeal cookies.

Answer:

x is not a number it can be a variable like 1x+2x=3x

Answer:

  B.  -75

Step-by-step explanation:

Consider segments AC and A'C'. Point A' is clockwise from point A by an amount less than 90°. Positive angles are measured counterclockwise, so this suggests the angle of rotation is about -75°.

__

In the attached, we have used the invariant point on segments AC and A'C' as the vertex of the angle we want to measure. The angle between the lines appears to be about 75°, matching the answer choices.

Answer:

let the angle be x

Step-by-step explanation:

then,

angle1=2x

angle2=4x

angle3=9x

sum of all angles i  triangle is 180

then

2x+4x+9x=180

15x=180

x=12

angle1=2*12=24

angle2=4*12=48

angle3=9*12=108

Answer:

correct

Step-by-step explanation:

Yes.

You multiply both 5 and 16 by the same number, 2, to get 10/32.

An expression for x in terms of a and b is y = b - 2x and an expression for y in terms of a and b is y = 2a - b.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, A system of equations x + y = a and 2x + y = b.

Now,

x + y = a.

x = a - y and y = a - x.

2x + y = b.

2x = b - y.

x = (b - y)/2.

y = b - 2x.

An expression for x in terms of a and b is,

x + y = a

x + b - 2x = a.

- x = a - b.

x = b - a.

An expression for y in terms of a and b is,

2(a - y) + y = b.

2a - 2y + y = b.

2a - y = b.

- y = b - 2a.

y = 2a - b.

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Answer:

Any value greater than -9 and less than -3

Step-by-step explanation:

Explained and uploaded

Answer:

Step-by-step explanation:

b² = a² + c² - 2ac × cos (m∠B)

b² = 105² + 9² - 2(9)(105)cos65°

b ≈ 101.5

Answer:

6(b + 20) ≥ 26

Step-by-step explanation:

6(b + 20) ≥ 26

Answer:

6(b + 20) ≥ 26

b ≥ -15 2/3

Step-by-step explanation:

6(b + 20) ≥ 26

6b + 120 ≥ 26

6b ≥ -94

b ≥ -15 2/3